Rewrite as a simplified fraction. ${2.\overline{67} = {?}}$
Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{aligned}100x &= 267.6767...\\ 1x &= 2.6767...\end{aligned}}$ Subtracting the two equations, we have: ${99x = 265}$ ${x = \dfrac{265}{99}} \text{or} {2 \dfrac{67}{99}}$